Ceballos is due to return to Spain following a season-long switch, though a report from the Evening Standard's James Olley indicates the Gunners are confident they can prolong the terms amid the uncertainty of when first-team activities will resume.
English league football is suspended until April 30 because of the coronavirus, and with clubs set to meet next month to discuss a more realistic return to action in mid-May, the season could theoretically be completed prior to June 30 as per UEFA's request.
Even so, Arsenal don't want to risk contesting the Premier League run-in and FA Cup pursuit without the influential Spanish international.
Olley reports that no formal discussions have been launched with Real, though Arsenal believe the club won't oppose an extension to Ceballos' loan terms.
At Ceballos' request, the 23-year-old's loan deal did not include a club option to buy, with reports in January suggesting that the eight-time capped La Roja international fancied a return to the Spanish capital following Unai Emery's sacking.
Following a recovery from a hamstring injury, Ceballos spoke glowingly of Emery's successor, Mikel Arteta, and appeared in each of Arsenal's last six matches in all competitions including a stellar showing against West Ham.